Research and Development Service, Veterans Affairs Greater Los Angeles Healthcare System Los Angeles, CA, USA ; Complex Biological Systems Alliance North Andover, MA, USA.
Front Mol Neurosci. 2014 Apr 17;7:29. doi: 10.3389/fnmol.2014.00029. eCollection 2014.
Grover's quantum (search) algorithm exploits principles of quantum information theory and computation to surpass the strong Church-Turing limit governing classical computers. The algorithm initializes a search field into superposed N (eigen)states to later execute nonclassical "subroutines" involving unitary phase shifts of measured states and to produce root-rate or quadratic gain in the algorithmic time (O(N (1/2))) needed to find some "target" solution m. Akin to this fast technological search algorithm, single eukaryotic cells, such as differentiated neurons, perform natural quadratic speed-up in the search for appropriate store-operated Ca(2+) response regulation of, among other processes, protein and lipid biosynthesis, cell energetics, stress responses, cell fate and death, synaptic plasticity, and immunoprotection. Such speed-up in cellular decision making results from spatiotemporal dynamics of networked intracellular Ca(2+)-induced Ca(2+) release and the search (or signaling) velocity of Ca(2+) wave propagation. As chemical processes, such as the duration of Ca(2+) mobilization, become rate-limiting over interstore distances, Ca(2+) waves quadratically decrease interstore-travel time from slow saltatory to fast continuous gradients proportional to the square-root of the classical Ca(2+) diffusion coefficient, D (1/2), matching the computing efficiency of Grover's quantum algorithm. In this Hypothesis and Theory article, I elaborate on these traits using a fire-diffuse-fire model of store-operated cytosolic Ca(2+) signaling valid for glutamatergic neurons. Salient model features corresponding to Grover's quantum algorithm are parameterized to meet requirements for the Oracle Hadamard transform and Grover's iteration. A neuronal version of Grover's quantum algorithm figures to benefit signal coincidence detection and integration, bidirectional synaptic plasticity, and other vital cell functions by rapidly selecting, ordering, and/or counting optional response regulation choices.
格罗弗的量子（搜索）算法利用量子信息理论和计算的原理，超越了控制经典计算机的强大丘奇-图灵限制。该算法将搜索场初始化为叠加的 N（本征）态，以便稍后执行非经典的“子程序”，涉及测量状态的幺正相移，并在算法时间（O(N^(1/2))) 中产生根速率或二次增益，以找到某些“目标”解 m。类似于这种快速的技术搜索算法，单细胞生物，如分化神经元，在搜索适当的储存操作钙（2+）反应调节中表现出自然的二次加速，其中包括蛋白质和脂质生物合成、细胞能量学、应激反应、细胞命运和死亡、突触可塑性和免疫保护等过程。这种细胞决策的加速是由于细胞内网络钙离子诱导的钙离子释放的时空动力学和钙离子波传播的搜索（或信号）速度。由于化学过程，如钙（2+）动员的持续时间，在储存器之间的距离上成为限速过程，因此钙离子波从缓慢的跳跃式到快速连续梯度的储存器间传播时间以与经典钙离子扩散系数 D^(1/2) 的平方根成比例的二次方式减少，与格罗弗量子算法的计算效率相匹配。在这篇假设和理论文章中，我使用储存操作细胞质钙离子信号的火灾-扩散-火灾模型详细阐述了这些特征，该模型适用于谷氨酸能神经元。与格罗弗量子算法对应的突出模型特征被参数化，以满足 Oracle Hadamard 变换和格罗弗迭代的要求。神经元版本的格罗弗量子算法有望通过快速选择、排序和/或计数可选的反应调节选择，从而有利于信号一致性检测和整合、双向突触可塑性和其他重要的细胞功能。
